Anisotropic exchange in ytterbium spinels

Recently, the possibility that competing strongly anisotropic exchange interactions may stabilize a range of unusual phenomena has attracted much interest. Examples include spin-orbit Mott insulators which may realize variants of Kitaev’s honeycomb model and quantum rare-earth pyrochlores which host order-by-disorder physics, strong multi-phase competition, and could potentially harbour a quantum spin ice ground state. In this talk, we consider exchange interactions in ytterbium pyrochlore spinels. These compounds have the same edge-sharing octahedra found in the Kitaev materials, but with the atomic physics and frustrated lattice of the rare-earth pyrochlores. We argue that the exchange in these compounds can be understood within the simple “charging approximation”. We then validate this framework on the well-characterized “breathing” pyrochlore Ba$_3$Yb$_2$Zn$_5$O$_{11}$, finding good agreement with the experimentally determined parameters. Turning to the Yb-based spinels, we find that the landscape of exchange parameters contains only two clear limits: a Heisenberg antiferromagnet and a ferromagnetic Kitaev exchange interaction. We further discuss the effect of relaxing the assumption of a perfect 90 degree bond angle and comment on applications to known Yb-based spinels.